1. Field of the Invention
The present invention relates generally to communications. Particularly, the present invention relates to frequency discrimination in a communications environment.
2. Description of the Related Art
CDMA communications systems typically use directional antennas located in the center of a cell and broadcasting into sectors of the cell. The antennas are coupled to base stations that transmit control the cells. The cells are typically located in major metropolitan areas, along highways, and along train tracks to allow consumers to communicate both at home and while traveling.
Even though both a mobile and a base station are transmitting on a frequency that is known to each, there are factors such as multipath errors and Doppler shift in the frequency that introduce errors in the frequency that is received. For example, if a mobile is approaching a base station, the Doppler effect increases the signal's frequency as observed by the base station. If the mobile is moving away from the base station, the base station observes a signal having a frequency that is less than the frequency transmitted by the mobile. The amount of frequency shift is a function of the speed of the mobile.
Another source of frequency error is the fact that the two local oscillators (one at the base station and one at the mobile that are used for generating the “clock” signal) can never be operating at exactly the same frequency. Typically, the mobile uses a less expensive local oscillator that can introduce a frequency error of up to 10 KHz when the carrier frequency is around 2 GHz.
During communication, the base station transmits a pilot channel that is received by the mobile. The pilot channel, comprised of pilot symbols, contains no information. The mobile utilizes the pilot symbols to generate time, frequency, phase, and signal strength references.
In some systems, the mobile also transmits a pilot signal. The mobile's pilot signal is then similarly used by the receiving base station to generate time, frequency, phase, and signal strength references relative to the mobile.
In order for a base station to communicate with a mobile on a certain frequency, both need to use a frequency discriminator in a frequency-tracking loop.
FIG. 1 illustrates a typical prior art frequency-tracking loop (FTL) 100. This figure shows a signal, Δf, entering a summer 101. Δf represents the frequency error present in an incoming signal of successive pilot symbols. The summer 101 subtracts from Δf an initial estimate Δ{circumflex over (f)}.
Frequency discriminator 105 is known and operates on the frequency error associated with successive pilot symbols. The value of each pilot symbol is herein represented by variable yk. The period of each symbol yk is denoted by TS.
An incoming sequence of pilot symbols are accumulated after input signal rotation to result in a residual frequency error, out of summer 101, equal to Δfres. A pilot symbol yk having residual frequency error Δfresk may be denoted as:yk=Aej2πTsΔfresk+nkwhere nk is the additive noise corrupting the kth symbol and A is a complex amplitude that is a function of, among other things, the current channel attenuation. It is assumed that fading is slow enough so that successive symbols have roughly the same complex amplitude.
A time constant (τ) is herein defined as the time it takes FTL 100 to converge to 1/e of an initial frequency error. A pull-in range conventionally defines a maximum initial frequency error for which FTL 100 is able to converge. A design goal is to minimize time constant τ, all the while maximizing the pull-in range, to maintain the standard deviation of the residual frequency error under steady-state conditions to within desirable levels.
A loop filter L(z) 110, series coupled to the output of frequency discriminator 105, is used to adjust the time constant τ, pull-in range, and standard deviation of the frequency error.
A known type of frequency discriminator 105 is a cross product discriminator, the operation of which may be expressed as Δfrescp=imag(ykyk−1*), with * denoting complex conjugation. From the above equation for yk and Δfrescp we getΔfrescp=|A|2 sin(2πTsΔfres)+n,
with n being a noise component. Thus as Δfres approaches 1/2Ts, the value of sin(2πTsΔfres) becomes smaller, resulting in the following condition:
First, the pull-in range of the FTL 100 is smaller than a theoretical pull-in range due to the effects of noise. Second, when the initial frequency error Δf is greater than ½ the theoretical pull-in range, FTL 100 takes a long time to converge to 1/e of the initial frequency error Δf.